Solving First Degree Equations

First Degree Equation: An equation characterized by having a single variable ... which may be repeated within the equation more than once ... which is raised to the first power. Note: plain variable "x" is the same as "x¹" ... plain variable "x" is the same as "x" raised to the first power.

A typical 1st degree equation is shown below ... together with the normal steps of solutions:

STEP 1:  Eliminate parenthesis (if any) by multiplying through using the distributive property.

STEP 2:  Eliminate fractions (if any) by finding the common denominator and multiplying the entire equation through by the common denominator. In this example, "12" is the common denominator. NOTE: Notice that the negative sign in front of the compound fraction "(5x - 3)/4" must be distributed through the entire numerator. You are subtracting the total fraction.

STEP 3: Combine like terms (if any) on both the left and right sides of the equation.

STEP 4:  Isolate "x" (or the variable being solved for) to one side of the equation ... and at the same time get non-"x" terms to the opposite side. In this example, you'd subtract "10x" from both sides of the equation (add "-10x" to both sides) ... and subtract "7" from both sides of the equation.

STEP 5:  Get "x" by its lonesome (get the variable all by itself). In this example, divide both sides of the equation by "5" (or, equivalent, multiply both sides of the equation by the fraction "1/5".

STEP 6 (optional): Once an answer is produced, it should be able to be substituted into the original equation ... and make it true. This is a method that can be used to "check" an answer.

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